Problem: Nauuo is a girl who loves playing chess.

One day she invented a game by herself which needs n chess pieces to play on a m× m chessboard. The rows and columns are numbered from 1 to m. We denote a cell on the intersection of the r-th row and c-th column as (r,c).

The game's goal is to place n chess pieces numbered from 1 to n on the chessboard, the i-th piece lies on (r_i,\,c_i), while the following rule is satisfied: for all pairs of pieces i and j, |r_i-r_j|+|c_i-c_j|≥|i-j|. Here |x| means the absolute value of x.

However, Nauuo discovered that sometimes she couldn't find a solution because the chessboard was too small.

She wants to find the smallest chessboard on which she can put n pieces according to the rules.

She also wonders how to place the pieces on such a chessboard. Can you help her?

Input

The only line contains a single integer n (1≤ n≤ 1000) — the number of chess pieces for the game.

Output

The first line contains a single integer — the minimum value of m, where m is the length of sides of the suitable chessboard.

The i-th of the next n lines contains two integers r_i and c_i (1≤ r_i,c_i≤ m) — the coordinates of the i-th chess piece.

If there are multiple answers, print any.

Examples

Input


2


Output


2
1 1
1 2

Input


4


Output


3
1 1
1 3
3 1
3 3

Note

In the first example, you can't place the two pieces on a 1×1 chessboard without breaking the rule. But you can place two pieces on a 2×2 chessboard like this:

<image>

In the second example, you can't place four pieces on a 2×2 chessboard without breaking the rule. For example, if you place the pieces like this:

<image>

then |r_1-r_3|+|c_1-c_3|=|1-2|+|1-1|=1, |1-3|=2, 1<2; and |r_1-r_4|+|c_1-c_4|=|1-2|+|1-2|=2, |1-4|=3, 2<3. It doesn't satisfy the rule.

However, on a 3×3 chessboard, you can place four pieces like this:

<image>

Solution (in JAVA):

Solution:
import java.io.BufferedInputStream;
import java.io.BufferedOutputStream;
import java.io.IOException;
import java.io.PrintStream;
import java.io.StreamTokenizer;
import java.util.HashMap;
import java.util.Scanner;

public class Main {
	@SuppressWarnings("deprecation")
	static StreamTokenizer st = new StreamTokenizer(new BufferedInputStream(System.in));
	static PrintStream p = new PrintStream(new BufferedOutputStream(System.out));
	static int bc[] = new int[20005];

	public static void main(String[] args) {
		Scanner sc = new Scanner(new BufferedInputStream(System.in));
		int n = sc.nextInt();
		int len = n/2+1;
		int x[] = new int[n+1];
		int y[] = new int[n+1];
		x[0] = 1;
		y[0] = 1;
		boolean flag = true;
		for(int i = 1;i<n;i++) {
			if(flag) {
				x[i] = x[i-1]+1;
				y[i] = y[i-1];
			}else {
				x[i] = x[i-1];
				y[i] = y[i-1]+1;
			}
			flag= !flag;
		}
		System.out.println(Math.max(x[n-1], y[n-1]));
		for(int i = 0;i<n;i++) {
			System.out.println(x[i]+" "+y[i]);
		}
		
	}

	static int find(int a) {
		if (bc[a] < 0)
			return a;
		return bc[a] = find(bc[a]);
	}

	static void union(int a, int b) {
		int l = find(a);
		int r = find(b);
		if (l == r)
			return;
		bc[l] = r;
	}

	static int nextInt() {
		try {
			st.nextToken();
		} catch (IOException e) {
			e.printStackTrace();
		}
		return (int) st.nval;
	}

	static long nextLong() {
		try {
			st.nextToken();
		} catch (IOException e) {
			e.printStackTrace();
		}
		return (long) st.nval;
	}

	static double nextDouble() {
		try {
			st.nextToken();
		} catch (IOException e) {
			e.printStackTrace();
		}
		return st.nval;
	}
}